Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 6$ $a_i = a_{i-1} + 4$ What is $a_{10}$, the tenth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $6$ and the common difference is $4$ To find the tenth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 6 + 4(i - 1)$ To find $a_{10}$ , we can simply substitute $i = 10$ into the our formula. Therefore, the tenth term is equal to $a_{10} = 6 + 4 (10 - 1) = 42$.